The 26-year-old suffered a dislocated shoulder earlier this month but looked set for a January return to action before his shoulder popped out again.
Former Oldham striker Josh Parker, who has joined the club on non-contract terms to provide back-up in Pittman's absence, could come into the squad.
Manager Chris Wilder will be without Adam Chapman, who fell awkwardly and injured his ankle in last week's 2-0 FA Cup victory over Accrington.
Michael Duberry came through his late return to action against Accrington unscathed having not played since May.
Simon Heslop was due to serve the last game of his three-match ban in Saturday's clash with Fleetwood, but since the game was called off due to a waterlogged pitch, he will be unavailable to face Exeter instead.